Preheat oven to 325°F. Spray a 9x13 inch pan with non-stick spray.
Toss the strawberries in ¼ cup flour. Set aside.
Sift together 2 and 1/4 cup flour, baking powder, baking soda, and salt. Add the lemon zest.
In the bowl of an electric mixer, beat the butter, coconut oil, and sugar until light and fluffy. Stop the mixer and scrape the sides.
Add the eggs one at a time. Beat until mixture is creamy and fluffy for about 2 minutes at medium speed. Stop the mixer at about 1 minute and scrape the sides.
Add the lemon juice.
Next, add flour mixture alternately with the yogurt, mixing until just incorporated. Fold in the strawberries by hand. Never overmix a cake after adding the flour or it will be tough.
Pour batter into pan and smooth the top.
Bake in preheated 350°F oven for 40 to 45 minutes or until a toothpick inserted in the center comes out clean.
Whisk powdered sugar, heavy cream, and food coloring together until smooth. This glaze needs to be thin and pourable. Add more heavy cream if needed. Pour over warm cake.